Maybe 300mA order of magnitude is more common than 3A, but it's not inconceivable. Lots of designs wake up, burst some RF data at a few hundred mA transceiver load for a few tens of microseconds, then go back to sleep for another few seconds. There are some long-interval scientific instruments that need high-speed ADCs or DACs on battery power in remote locations, which might get into higher current than a few hundred mA. Some deep space crafts can sleep at very low power and run their transmitters at comparable currents. It's very situational.